Bird Person, a game that is exceptionally difficult and very hard to get good at is quite possibly the best kind of game, because of the great feeling of accomplishment you get when you finally do overcome that obstacle - whether it be an optional boss, such as Panthera Cantus, or the final section or stage of a long game, or just a tough song in your rhythm game of choice. It's all about the feeling of having pushed yourself to your gaming limits - and possibly even beyond - and having come out on top. This is part of why I like shoot-'em-ups a lot, especially those with end sequences that make the rest of the game look like a cakewalk (see: stage 8 in Gradius Galaxies) and those normally classified as "danmaku" - most games in the genre have retained the immense difficulty from the days when arcade games needed to be difficult to make money properly, and that type and level of insanity is exactly what I like in a game.
By this train of thought, the worst kinds of game are those that are impossible to be anything close to good at no matter what you do, ever (to the point where cheating becomes necessary), and those that are too easy despite their reputation. In the first case, an example would be any game-ending-glitch-ridden game; the game I'm mainly thinking of for the latter is the DS version of N+, perhaps a bit unfairly since I'm more used to handheld platforming than doing so on PC. Avoid the former at all costs, and see if you're just overlooking an item in an options menu or something for the latter, or, if possible, check if you set something when you started - it might just be too easy because the game's difficulty level is actually set to easy.
Yes, I'm well aware of the fact that there are games that are played for reasons other than a challenge, and this doesn't take those into account. If you want to play a game doing what Lizard Dude recently described as taking the artsy-fartsy route to send your mind soaring, then by all means go ahead - I'd be a hypocrite if I raised a finger to stop you. However, if you're playing a "normal" video game on the easiest difficulty possible every time and breezing through it like it's nothing, don't just keep playing that *******ization of a game forever. Move up. Start owning for real. If you think the higher difficulties are too hard, just keep on trying. Don't give up after a few tries and be forever doomed to n00bdom.
More than any of that, though, remember to have fun. If you don't think shattering the wall of what you think you alone can do as a gamer is fun, then don't necessarily try to do it right away. Play slightly easier games, or, if the game you're sucking at supports it, team up with some friends. These together have two effects - your skill as a gamer will increase, and unless your friends are exactly like you in every possible way, you'll see different strategies - and one of them just might be the right one for you to finally succeed when you go at it alone.
Go. Play some games. Rather than complaining that a game is "too hard" or complaining about people thinking games being too hard is a good thing, have some fun.
On the subject of Mario RPGs...no vote. The only one I ever got around to finishing was SMRPG, and that was ages ago, so I don't remember much of the game. I liked the bits of Paper Mario and TTYD that I've played, but I can't draw a conclusion just from that. I almost finished Superstar Saga, but lost interest at some point. I have a feeling I'll decide to go back and finish it eventually, but then I'll have also decided that I want to play through the whole thing again. If this thread is still around once I've at least done that, I might be able to make a decision.